On the use of statistics in complex weather and climate models

1. On the use of statistics in complex weather and climate models Andreas Hense Meteorological Institute University Bonn Spruce VI

2. Together with.. • Heiko Paeth (Bonn) • Seung-Ki Min (Seoul) • Susanne Theis (Bonn) • Steffen Weber (Bonn, WetterOnline) • Monika Rauthe (Bonn, now Rostock) • Rita Glowienka-Hense Spruce VI

3. Overview • Some general remarks concerning complex models of the atmosphere / the climate system and statistics • Use of statistics in numerical weather prediction • ensemble prediction • calibration • Use of statistics in climate change simulations • Defining a signal and its uncertainty • Detecting a signal in observations Spruce VI

4. Climate Simulation and Numerical Weather Prediction • Randomness in the climate system / atmosphere originates from highdimensionality and nonlinear scale interactions • Randomness in climate models and NWP models arises additionally • from parametrizations • from model selection and construction Spruce VI

5. Climate Simulation and Numerical Weather Prediction • Modelling a high dimensional system requires scale selection in space and time  • Simulation time T <  a NWP / inital condition problem • T >>  climate problem • Urban/Micro climatology T ~ 1 d,  ~ min or h • climate simulations embedded into NWP • detailed precipitation with T ~ 10 d Spruce VI

6. Climate Simulation and Numerical Weather Prediction • The deterministic view • e.g. wrong NWP forecast due to model errors • e.g. Any modeled climate change in a climate simulation with perturbed greenhouse gase forcing is due to this external forcing. • More illustrative: • „We predict in two days advance the sunny side of the street“ • „We predict in two days advance which tennis court in Wimbledon will have rain“ Spruce VI

7. Climate Simulation and Numerical Weather Prediction • General formulation of the problem • Analysis of the joint pdf of simulations m and observations o • p(m|o) for model validation and selection • description of the observation process, mapping of o on m with some unknown parameterset  • maximize p(m,  | o): calibration, model output statistics MOS Spruce VI

8. NWP examples • The generation of model ensemble • with precipitation as a (notoriously) difficult variable • generation of precipitation is at the end of a long chain of interactions • involves scales from the molecular scale up to relevant atmospheric scales 1000 km • highly non Gaussian • positive definite • most probably fat tailed Spruce VI

9. Generation of NWP ensembles • Sampling uncertainty in initial conditions • Sampling uncertainty in boundary conditions • physical bc at Earth‘s surface • numerical bc • Sampling uncertainty in parameter constellations • Using the limited area weather forecast model of the German Weather Service DWD (7km * 7km, 35 vertical layers, 177 * 177 gridpoints) Spruce VI

10. Numerical weather prediction is a scenario description of future states of the atmosphere Spruce VI

11. Sampling of parameter uncertainty:NWP models become stochastic models Spruce VI

12. Sampling uncertainty in initial conditions Most probably not a correct sampling ! Spruce VI

13. Deterministic forecast 10 member ensemble std deviation Spruce VI

14. Experimental verification, mean Spruce VI

15. Calibration of weather forecasts MOS • Weather forecasts NMC on a 1° * 1° grid • single station observations every three hours • not a fully developed Bayesian scheme yet • but • multiple correlation with stepwise regression to select large scale predictands • and cross validation Spruce VI

16. Calibration error statisticsmean square error Spruce VI

17. Calibration error statistics, explained variance Spruce VI

18. Application: Daily Tmax Winter 2001/02 Obs MOS error Spruce VI

19. Climate change model simulations • Predicting changes of climate statistics p(m,t) due to changes in physical boundary conditions • changes in p(m,t) relative to p(m,t0) due to increasing greenhouse gase concentrations e.g. CO2 (t) and other anthropogenic forcings • changes in p(m,t) relative to p(m,t0) due to solar variability, volcanic eruptions (natural forcings) • distinguish between anthropogenic and natural forcing effects Spruce VI

20. Climate change model simulationclassical view • Compare modeled anthropogenic changes with observed changes • if projection of observed changes onto modeled changes are larger than an unforced background noise level: reject Null hypothesis of unforced climate variability • requires the assumption of a „significant“ model change • which time/space scales and variables allow for these significant changes? Spruce VI

21. Climate change simulation with GHG forcing • Sampling uncertainty in initial conditions • ensemble simulations (typically 5 or 6 members) • Sampling inter-model uncertainty • two model example: ECHAM3/T21 and HADCM2 • multimodel example: 15 different models from IPCC data server Spruce VI

22. Climate change simulations with GHG forcing • Two model case: precipitation and near surface temperature • multi model case: Arctic oscillation/North Atlantic oscillation as a driving agent for regional climate variability in Europe • classical 2-way analysis-of-variance • x i,l,k = a + b j + c l + d i,l + e i,l,k • b i : common GHG signal as function of time i • c l : bulk inter-model differences • d i,l : inter model-differences in GHG forcing Spruce VI

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29. Climate change model simulationsBayesian view • Available a set of hypothesis /scenarios hi • unforced variability i=1 • GHG forced • GHG + sulphate aerosol forced • solar/volcanic forced • for each hypothesis / scenario we have a prior  (hi ) • Selection of hi based on a given observation • computation of Bayes factor from likelihood • decision based on posterior p(hi|o) Spruce VI

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31. Climate change model simulationsBayesian view • 2-dimension example: using Northern hemisphere mean temperatures near surface and lower stratosphere • observations 1979 - 1999 moving annual means • model signal: linear change between 1990-2010 in model year 2000 • 5 member ensemble ECHAM3/T21 GHG only • 3 member ensemble ECHAM3/T21 GHG+S-Ae Spruce VI

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36. Conclusion • Weather prediction and climate system models simulate parts of the real Earth system • starting from these complex models: need to introduce statistical aspects at various levels • starting from observations: pure data-based models need a guidance: use physics / chemistry of complex models • we need quantitative statements about future changes and their uncertainties of the real system either the next day, the next decade or century Spruce VI

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